Electrodynamics/Ampere's Law

In physics, Ampère's Circuital law, discovered by André-Marie Ampère, relates the circulating magnetic field in a closed loop to the electric current passing through the loop. It is the magnetic equivalent of Gauss's Law.

James Clerk Maxwell conceived of displacement current as a polarization current in the dielectric vortex sea which he used to model the magnetic field hydrodynamically and mechanically. He added this displacement current to Ampère's Circuital law at equation (112) in his 1861 paper On Physical Lines of Force.

The generalized law, as corrected by Maxwell, takes the following integral form:

[Ampere-Maxwell Law]

where in linear media

is the displacement flux density (in coulombs per square meter).

This Ampère-Maxwell law can also be stated in differential form:

where the second term arises from the displacement current.

With the addition of the displacement current, Maxwell was able to postulate (correctly) that light was a form of electromagnetic wave. See Electromagnetic wave equation for a discussion on this important discovery. We will discuss all of Maxwell's laws in a later chapter.

The Equivalent to Gauss's Law for Electricity is Ampère's Law in Magnetism. It's a bit more complicated and you should know Gauss's before getting a grip on this one.

Imagine a wire with current flowing through it, the right hand screw rule says that there will be a magnetic field curling around the way your fingers do with your thumb pointing the direction of conventional current.

You can predict that the magnetic field will be curling around proportionally to the current flowing. Ampère's Law will tell you how.